Gaussian basis sets violate nuclear cusp conditions [492, 493, 494]. This may lead to large errors in wavefunction at nuclei, particularly for spin density calculations [495]. This problem can be alleviated by using an averaging operator that compute wavefunction density based on constraints that wavefunction must satisfy near Coulomb singularity [496, 497]. The derivation of operators is based on hyper virial theorem [498] and presented in Ref. Rassolov:1996b. Application to molecular spin densities for spin-polarized [497] and DFT [499] wavefunctions show considerable improvement over traditional delta function operator.

One of the simplest forms of such operators is based on the Gaussian weight function that samples the vicinity of a nucleus of charge located at . The parameter has to be small enough to neglect two-electron contributions of the order but large enough for meaningful averaging. The range of values between 0.15–0.3 *a.u.* is shown to be adequate, with final answer being relatively insensitive to the exact choice of [496, 497]. The value of is chosen by RC_R0 keyword in the units of 0.001 *a.u.* The averaging operators are implemented for single determinant Hartree-Fock and DFT, and correlated SSG wavefunctions. Spin and charge densities are printed for all nuclei in a molecule, including ghost atoms.

RC_R0

Determines the parameter in the Gaussian weight function used to smooth the density at the nuclei.

TYPE:

INTEGER

DEFAULT:

0

OPTIONS:

0

Corresponds the traditional delta function spin and charge densities

corresponding to

a.u.

RECOMMENDATION:

We recommend value of 250 for a typical spit valence basis. For basis sets with increased flexibility in the nuclear vicinity the smaller values of also yield adequate spin density.